THE FLOW OF WATER IN DRAIN TILE. 11 



in which Vincent gives values for the variable coefficient, K, ranging 

 from 0.75 for 2-inch tile to 0.875 for 6-inch tile. 

 Friedrich 1 states that Professor Gieseler's formula, 



V= 36.22 -y/W (6) 



is the best in practice as well as the simplest. 



Formula 6 is said by Professor Luedecke to have been deduced as 

 early as 1852 by the agricultural engineer Stocken, at Schweidnitz, 

 from Prony's formula, which is 



7=47.63V^7 (7) 



Beardmore's, sometimes called Leslie's, formula, 



V= 100 tJW (8) 



is similar to Chezy's, the coefficient C being taken as a constant, 100. 

 The Williams-Hazen general formula for all kinds of pipes is 



7= 6V2°- 6 V- 54 0.001- - 04 (9) 



This formula is of special importance in this discussion, since careful 

 comparison of it with the Chezy-Kutter formula has been made. 



C. G. Elliott, a widely known drainage authority, has modified the 

 Poncelet or Hawkesley formula as follows: 2 



' 7 = 48 Vtot (10 > 



for use on systems where the soil is open; 



■ / z?(a+-|) 



V 1+54 D 



F=48 r / ^ \ ,0 ^TJ (11) 



V i+ 



for use on large systems in close soil; 



7=48-1/ ^4)+^ (12) 



V Z+54Z? 



for use on large systems in open soil. 



The last term in the numerator under the radical in formulae 10 

 and 12 has been added to allow for the water pressure in the soil above 

 the tile drain. This additional head, however, is constantly varying, 

 being greatest when the earth is completely saturated. It is doubtful 

 whether it should be used in computing the discharge of a drain, and 

 if so, then only in open, porous soils. 



1 Friedrich, Kulturtechnischer Wasserbau, vol. 1, Berlin, 1912, p. 343. 



2 C. G. Elliott, Engineering for Land Drainage, New York, 2d ed., 1912, p. 93. 



